1. Field of the Invention
The present invention relates generally to a method of modeling the power distribution within the core of a nuclear reactor and more particularly to a method for designing initial and reload cores for a nuclear reactor.
2. Description of the Prior Art
The primary side of nuclear reactor power generating systems which are cooled with water under pressure comprises a closed circuit which is isolated and in heat-exchange relationship with a secondary side for the production of useful energy. The primary side comprises the reactor vessel enclosing a core internals structure that supports a plurality of fuel assemblies containing fissile material, the primary circuit within heat exchange steam generators, the inner volume of a pressurizer, pumps and pipes for circulating pressurized water; the pipes connecting each of the steam generators and pumps to the reactor vessel independently. Each of the parts of the primary side comprising a steam generator, a pump and a system of pipes which are connected to the vessel form a loop of the primary side. The primary side is also connected to auxiliary circuits, including a circuit for the volumetric and chemical monitoring of the pressurized water. The auxiliary circuit, which is arranged branching from the primary circuit, makes it possible to maintain the quantity of water in the primary circuit by replenishing, when required, with measured quantities of water, and to monitor the chemical properties of the coolant water, particularly its content of boric acid, which is important to the operation of the reactor.
For the purpose of illustration, FIG. 1 shows a simplified nuclear reactor primary system, including a generally cylindrical reactor pressure vessel (10) having a closure head (12) enclosing a nuclear core (14). A liquid reactor coolant, such as water is pumped into the vessel (10) by pump 16 through the core (14) where heat energy is absorbed and is discharged to a heat exchanger (18), typically referred to as a steam generator, in which heat is transferred to a utilization circuit (not shown), such as a steam driven turbine generator. The reactor coolant is then returned to the pump (16), completing the primary loop. Typically, a plurality of the above described loops are connected to a single reactor vessel (10) by reactor coolant piping (20).
An exemplary reactor design is shown in more detail in FIG. 2. In addition to the core (14) comprised of a plurality of parallel, vertical, co-extending fuel assemblies (22), for purposes of this description, the other vessel internal structures can be divided into the lower internals (24) and the upper internals (26). In conventional designs, the lower internals function is to support, align and guide core components and instrumentation, as well as direct flow within the vessel. The upper internals restrain or provide a secondary restraint for the fuel assemblies (22) (only two of which are shown for simplicity in this figure), and support and guide instrumentation and components, such as control rods (28). In the exemplary reactor shown in FIG. 2, coolant enters the reactor vessel (10) through one or more inlet nozzles (30), flows down through an annulus between the vessel and the core barrel (32), is turned 180° in a lower plenum (34), passes upwardly through a lower support plate (37) and a lower core plate (36) upon which the fuel assemblies (22) are seated and through and about the assemblies. In some designs the lower support plate (37) and the lower core plate (36) are replaced by a single structure, the lower core support plate, at the same elevation as (37). The coolant flow through the core and surrounding area (38) is typically large, on the order of 400,000 gallons per minute at a velocity of approximately 20 feet per second. The resulting pressure drop and frictional forces tend to cause the fuel assemblies to rise, which movement is restrained by the upper internals, including a circular upper core plate (40). Coolant exiting the core (14) flows along the underside of the upper core plate and upwardly through a plurality of perforations (42). The coolant then flows upwardly and radially to one or more outlet nozzles (44).
The upper internals (26) can be supported from the vessel or the vessel head and include an upper support assembly (46). Loads are transmitted between the upper support assembly (46) and the upper core plate (40), primarily by a plurality of support columns (48). A support column is aligned above a selected fuel assembly (22) and perforations (42) in the upper core plate (40).
Rectilinearly moveable control rods (28) typically include a drive shaft (50) and a spider assembly (52) of neutron poison rods that are guided through the upper internals (26) and into aligned fuel assemblies (22) by control rod guide tubes (54). The guide tubes are fixedly joined to the upper support assembly (46) and connected by a split pin (56) forced fit into the top of the upper core plate (40). The pin configuration provides for ease of guide tube assembly and replacement if ever necessary and assures that core loads, particularly under seismic or other high loading accident conditions are taken primarily by the support columns (48) and not the guide tubes (54). This assists in retarding guide tube deformation under accident conditions which could detrimentally affect control rod insertion capability.
FIG. 3 is an elevational view, represented in vertically shortened form, of a fuel assembly being generally designated by reference character (22). The fuel assembly (22) is the type used in a pressurized water reactor and has a structural skeleton which, at its lower end includes a bottom nozzle (58). The bottom nozzle (58) supports the fuel assembly (22) on a lower core support plate (36) in the core region of the nuclear reactor. In addition to the bottom nozzle (58), the structural skeleton of the fuel assembly (22) also includes a top nozzle (62) at its upper end and a number of guide tubes or thimbles (54), which extend longitudinally between the bottom and top nozzles (58) and (62) and at opposite ends are rigidly attached thereto.
The fuel assembly (22) further includes a plurality of transverse grids (64) axially-spaced along, and mounted to the guide thimbles (54) and an organized array of elongated fuel rods (66) traversely-spaced and supported by the grids (64). Also, the assembly (22) has an instrumentation tube (68) located in the center thereof and extending between, and mounted to, the bottom and top nozzles (58) and (62). With such an arrangement of parts, fuel assembly (22) forms an integral unit capable of being conveniently handled without damaging the assembly of parts.
As mentioned above, the fuel rods (66) in the array thereof in the assembly (22) are held in spaced relationship with one another by the grids (64) spaced along the fuel assembly length. Each fuel rod (66) includes nuclear fuel pellets (70) and is closed at its opposite ends by upper and lower end plugs (72) and (74). The pellets (70) are maintained in a stack by a plenum spring (76) disposed between the upper end plug (72) and the top of the pellet stack. The fuel pellets (70), composed of fissile material, are responsible for creating the reactive power of the reactor. The fuel pellets (70) within a given fuel rod (66) within an assembly (22) may vary in composition and enrichment from other fuel rods (66) within the same fuel assembly (22). It is important to manage the axial and radial power profile of the core because the power output of the reactor is limited by the hottest temperature experienced along a fuel rod (66). There is a need to keep the operating conditions below that which will result in a departure from nucleate boiling along the cladding of the fuel rod (66). Under that type of condition the heat transfer from the fuel rod (66) to the adjacent coolant deteriorates raising the temperature of the fuel rod which can result in cladding failure. Thus, the placement of the different types of fuel rods within a fuel assembly (22) and the placement of the different types of fuel assemblies within the core (14) is very important to assure safety and maximize the efficiency of the core output. A liquid moderator/coolant such as water or water containing boron, is pumped upwardly through a plurality of flow openings in the lower core support plate (36) to the fuel assembly (22). The bottom nozzle (58) of the fuel assembly (22) passes the coolant upwardly through the guide tubes (54) and along the fuel rods (66) of the assembly in order to extract heat generated therein for the production of useful work.
To control the fission process, a number of control rods (78) are reciprocally moveable in the guide thimbles (54) located at predetermined positions in the fuel assembly (22). Specifically, a rod cluster control mechanism (80) positioned above the top nozzle (62) supports the control rods (78). The control mechanism has an internally threaded cylindrical hub member (82) with a plurality of radially-extending flukes or arms (52). Each arm (52) is interconnected to the control rod (78) such that the control rod mechanism (80) is operable to move the control rods (78) vertically in the guide thimbles (54) to thereby control the fission process in the fuel assembly (22), under the motive power of control rod drive shafts (50) which are coupled to the control rod hubs (80), all in a well known manner.
As previously mentioned, it is important to manage the design of the initial and refueled cores to manage the axial and radial power distribution of the core to assure safety and maximize the efficiency of reactor operation. That means that the kinds of fuel rods (66) within an assembly (22) and the placement of those fuel rods as well as the placement of the assemblies within the core have to be carefully taken into account to minimize the temperature gradient experienced within the core. Presently, core designs are developed using neutron diffusion codes such as ANC, licensable from Westinghouse Electric Company LLC, Pittsburgh, Pa., the assignee of this application. These neutron diffusion codes divide the neutron energy into a few energy ranges (energy groups) and estimate the power distribution from core models. The accuracy of these estimates is not considered high enough due to inherent approximations in the geometric model of the system and the nuclear cross-section databases that they employ. Current reactor core analysis calculations typically use advanced nodal methods which homogenize the fuel pins in a fuel assembly into large nodes (for example, a 17 by 17 fuel rod assembly is transformed into a 2×2 nodal model as shown in FIG. 4. For a nuclear core, containing more than a 100 fuel assemblies, the three-dimensional neutron flux and power distributions are then calculated using the nodal model. Based upon the core-wide nodal power distribution, the assembly fuel pin (i.e. fuel rod) by fuel pin distributions are generated by combining a homogeneous solution with detailed form factors. This works well as long as the operational history can be modeled explicitly in the assembly calculations which generate the homogenized data and form factors. Unfortunately, the real operational history of each fuel assembly is not known in advance, which makes it difficult to generate the right form factors to accurately simulate the core.
Under actual core operating conditions, even for the same type of fuel assembly (22), the heterogeneity, i.e. the point-by-point flux and power distribution, will be changing during operation as a result of the surrounding environment and in particular the control rod insertion and withdrawal history. In order to capture the real history effect on fuel rod pin power, the prior art has tried many kinds of corrections to the pin power form factors with very complicated calculations employed to generate the fuel assembly data. However, the results are still far from satisfactory, especially when control rod or gray rod insertion and withdrawal is commonly experienced during normal power operation. This becomes a big and very difficult issue in the design of BWR cores and new designs of PWR cores, such as the AP1000 currently offered by Westinghouse Electric Company LLC. These problems arise because it is not known in advance when, where, and in which assemblies the control rods will be inserted. The history used to reflect the assembly data generated for the core design may be quite different from the real fuel history experienced in the core during normal operation and this difference is hard to capture in the core design codes using conventional methods.
Accordingly, a new methodology is desired that will better predict the power and flux distribution within the core of a nuclear reactor.
More particularly, a new methodology is desired that will predict the power and flux distribution axially, and radially, over the core taking into account each fuel element.
Furthermore, a new methodology is desired that will better predict the power distribution over a core of a nuclear reactor that more accurately reflects the history of the core.
Additionally, a new methodology is desired that will predict the power distribution within the core of a nuclear reactor without requiring extensive computer processing time or memory.